Torque and Drag in Directional Wells-Prediction and Measurement C.A. Johancsik, * SPE, Exxon Production Research CO. D.B. Friesen, ** Exxon Production Research Co. Rapier Dawson, SPE, Exxon Production Research Co.

Summary A computer model has been developed to predict drill-string torque and drag, and a versatile rotary torque meter has been built to use in calibrating the model. The principle of the predictive model is that torque and drag forces in a directional wellbore are primarily caused by sliding friction. Sliding friction force is calculated by multiplying the sidewall contact force by a friction coefficient.

Realistic sliding friction coefficients were determined from field data by using the same predictive computer model. These field data were gathered using novel torque and hookload indicators that are accurate, por-table, and easily installed. Good agreement between fric-tion coefficients calculated from different loads in the same well, as well as agreement between those for dif-ferent wells, indicates the validity of the predictive drillstring model. Sliding friction is concluded to be the major source of torque and drag in directional wells. For waterbase mud systems, typical friction coefficients range from 0.25 to 0.40.

Introduction Drillstring drag is the incremental force required to move the pipe up or down in the hole; torque is the moment re-quired to rotate the pipe. Drag forces usually are given relative to the string weight measured with the string rotating but not reciprocating. Measured from the rotating string weight, the pickup drag usually is slightly greater than the slack-off drag. The magnitudes of torque and drag are related in any particular well; high drag forces and excessive torque loads normally occur together.

There are a number of causes for excessive torque and drag, including tight hole conditions, sloughing hole, keyseats, differential sticking, cuttings buildup caused by poor hole cleaning, and sliding wellbore friction. With the exception of sliding friction, these causes are associated with problem conditions in the wellbore. Con-versely, in wells with good hole conditions, the primary source of torque and drag is sliding friction.

Torque and drag from any source tend to be more troublesome in directional holes. In very deep, highly deviated wells overcoming torque and drag can be critical to the successful well completion.

The capability to predict frictional loads on drill pipe

Now with Esso Resources Canada Ltd. "Now with Esso E&P Norway Inc.

01492136/84/0061-1380$00.25 Copyright 1984 Society of Petroleum Engineers of AIME

JUNE 1984

has two main benefits. First, deep, highly deviated wells can be planned to minimize torque and drag. Use of torque and drag as criteria to select the most appropriate well path will help ensure successful drilling operations to total depth. Second, more complete knowledge of drillstring loading allows use of improved drill string design techniques. Drillstring components can be chosen by using a systematic approach that considers the extra forces involved.

Torque and Drag Prediction Technique Mathematical Model. A lumped-parameter model pro-vides the basis for the prediction of torque and drag. Both torque and drag are assumed to be caused entirely by sliding friction forces that result from contact of the drill string with the wellbore. Other less important sources of torque and drag are not considered in this model.

Two factors affect sliding wellbore friction-the nor-mal contact force and the coefficient of friction between the contact surfaces. The product of these two factors represents the magnitude of the sliding friction force.

The normal contact force between the pipe and hole wall depends on several factors. This paper considers on-ly two contributions to normal force-the effects of gravity on the pipe and the effects of tension acting through curvatures in the wellbore. These forces, and their contributions to normal force, are shown schematically in Fig. 1. Other factors such as pipe bend-ing may contribute small normal forces but are not con-sidered here.

The sliding friction coefficient is the ratio of the fric-tion force to the normal contact force. In reality, this value depends on specific contacting materials and on the degree of lubrication at various places in the wellbore. However, in this paper all these effects are ex-pressed as a single characteristic friction coefficient representing average conditions in a particular wellbore. Determination of this lumped-parameter coefficient is fundamental to practical application of this model. Computer Calculations. The following paragraphs describe the calculation of torque and/or drag forces when the sliding friction coefficient is given. This calculation is made directly. The reverse calculation, where a friction coefficient is determined from given torque or drag data, is done by assuming a friction coef-ficient and iterating to match the data. In either case, drill string description and wellbore survey data are required.

987

Fig.1-Force balance on drillstring element illustrating sources of normal force.

Once the drillstring description, sUlVey data, and fric-tion coefficient are specified, the calculation starts at the bottom of the drill string and proceeds stepwise upward. Each short element of the drill string contributes small in-crements of axial and torsional load to running totals in the control program. Calculation of these load in-crements is the heart of the whole calculation.

Calculation of the normal force is the first step in calculating the load increments for an element of the drillstring. Fig. 2 shows the forces acting on a short, slightly cUlVed element. The net normal force, F n' is the negative vector sum of normal components from the weight, W, and from the two tension forces, Ft and F t +f1Ft . Even though the axis of the element is as-sumed to be an arc of a circle, this circle is not usually vertical and therefore the net normal force is not usually in the vertical plane. Fortunately, the friction calculation requires only the magnitude of the normal force, not its direction. The magnitude of the normal force is

The equation for normal force leads immediately to equations for the tension increment:

f1Fr=Wcos8 pPn , ....................... (2)

and for the torsion increment: f1M=JkFn r. . ............................. (3)

In Eq. 2, the plus or minus sign allows for pipe motion either up or down; the plus sign is for upward motion where friction adds to the axial load and the minus sign is for downward motion where the opposite is the case. In presenting data, this sign often is carried with the friction coefficient, so that a negative value identifies coeffi-cients calculated from slack-off drag measurements.

Eqs. 1 through 3 would be exact if applied to in-finitesimal elements of the drillstring. Use of longer

988

Fig. 2-Forces acting on drillstring element during pickup.

elements introduces small errors caused by neglecting second-order terms. For example, Eq. 1 uses the tension at the bottom of the element and assumes that tension does not change over the length of the element. First-order approximations are appropriate here because the underlying problem is complex. Predicting drill string drag is a three-dimensional belt friction problem with gravity; no closed-form solution for this problem exists except for special cases where f1a=O or W=O.

The errors introduced by Eqs. 1 through 3 are small if the CUlVature of each drillstring element is small. In test calculations with typical sUlVey data, changing from I-to 100-ft [0.3- to 30.S-m] elements produced only about a 1 % change in the overall results. All the calculations discussed in this paper were made with the drill string divided into roughly 100-ft [30.S-m] elements.

The best way to choose drill string element lengths is to use the basic sUlVey data stations to establish the calcula-tion intelVals. When intermediate calculation points are desired-for example, at a change in drill string proper-ties-a linear interpolation can be made. With this ap-proach, sUlVey inaccuracy probably contributes more er-ror to the results than approximations in the computer model.

Calibration of the Model. Before being used for torque and drag prediction, the computer model must be calibrated. Specifically, calibration involves a realistic determination of typical average sliding wellbore friction coefficients.

Realistic friction coefficients can be calculated from actual drilling situations by using the computer program with drillstring surface loads as input data to calculate the friction coefficient for a particular well geometry and drillstring. Input data include pickup weight, slack-off weight, and torque readings, each of which can produce an independent friction coefficient. Agreement among the three coefficients from one well not only lends credibility to the model but also provides confidence in

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the friction coefficient for its use in prediction of torque and drag when subsequent wells are planned.

It is believed that friction coefficients will depend largely on mud type and whether a hole is predominantly cased or open. Thus, friction coefficients from a number of similar wells must be compared to verify useful values for prediction use. This requires collection of a signifi-cant amount of field data for statistical comparison.

Field readings, to be reduced to wellbore friction coef-ficients, must be accurate and in useful units. This in-cludes both torque and drag data; torque must be in foot-pounds force or Newton-meters rather than in amperes or percent. Also, the friction calculation is enhanced by the use of accurate survey data. The directional well descrip-tion and the drillstring configuration are obtained easi-ly-accurate surface loads are not. Field Measurement of Torque and Drag The ability to obtain accurate field readings of drill string loads depends largely on the accuracy of the measure-ment equipment. Most rigs are well equipped to measure weights; few are capable of accurately measuring rotating torque.

To ensure high-quality field data, two special tools have been designed and built, one for tension and one for torque. Both devices can be used for direct measurement or as calibration instruments to verify rig torque and drag readings accurately. Drag Measurements. Almost all drilling rigs have a weight indicator to provide the operator with string weight, weight on bit (WOB) , and drag and overpull forces. The weight indicator normally is both accurate and repeatable. However, the force is sensed at the drill-ing line and includes the weight of the traveling equip-ment and the kelly. To analyze drag forces, the tensions at the top of the drill pipe , below the kelly, are required. Thus, it is necessary to subtract the weight of the travel-ing equipment when string weights are recorded.

There are several potential sources of error in rig drag readings. Zero offset in the instrument and inaccurate knowledge of total traveling equipment weights are two sources. The best way to eliminate these errors is to calibrate the weight indicator with a load cell placed below the kelly and traveling equipment. Weight Indicator Calibration Sub. A short drill collar sub was machined, instrumented, and calibrated to pro-vide accurate tensile readings over the range of to 500,000 lbf [0 to 2 224 kN] with less than 0.5% error. The sub is 30 in. [76.2 cm] long with NC50 connections. A machined-down area in the center is instrumented with strain gauges in a conventional four-arm, 350-ohm Wheatstone bridge arrangement. A protector cover, at-tached only above the gauge area, protects the gauges and houses a plug-in-type connector. Strain readings are monitored using conventional strain readout equipment. The sub was calibrated on an accurate tensile testing machine to 500,000 lbf [2 224 kN]. The weight in-dicator calibration sub is shown in Fig. 3.

Use of this device involves making up the sub between the kelly saver sub and the top joint of drillpipe. With slips set on the drillpipe, the blocks are hoisted in small weight increments up to full string weight. Readings from both the weight indicator and the calibration sub are recorded and plotted to produce a calibration curve. This

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Fig. 3-Weight indicator calibration sub.

calibration relates weight indicator readings to actual tension at the top of the drillstring.

Drillstring pickup drag readings are taken by hoisting the string slowly and recording the weight indicator reading. Similarly, slack-off drag is recorded while run-ning in slowly, and the rotating string weight is recorded while rotating without reciprocating the pipe. These readings then are adjusted according to the calibration curve to give actual loads at the top of the drill string for use in the computer program.

Torque Measurements. Measurement of rotary drilling torque presents a problem, primarily because it is dif-ficult to sense and communicate torque from a rotating piece of machinery. Most drilling rigs are equipped with some simple method for indicating torque. However, few of these techniques are accurate, and most devices are not calibrated to provide readings in useful torque units.

A few drilling rigs in the world are equipped with calibrated rotary torque indicators. Even when they work well, these devices lack portability. A portable torque meter can be taken from rig to rig as needed and can be easily returned to a shop for recalibration or repair. 1

Portable Torque Meter Design. To collect torque data from several rigs, it was necessary to design a portable device to measure torque in absolute torque units with a range up to 50,000 ft-Ibf [67 kN m]. An important con-sideration was the ease of installation without customiz-ing conventional rig components. Also, the device had to withstand the rugged working environment.

The concept of a portable torque-measuring device in-volved choice of a placement location in the torque path, a method for sensing torque, and a technique to com-municate readings in a suitable readout display. These problems were solved in the following way. The torque meter is designed to fit in the torque path between the rotary table and the kelly bushing (KB). Torque is con-tinuously sensed internally with strain gauges, and the data are communicated by a frequency-modulated (FM) datal ink to a receiver and display unit.

The prototype torque meter is designed to adapt to a 27V2-in. [70-cm] pin drive system. Its configuration is

989

Fig. 4-Rotary torque meter.

that of a 4 V2-in. [11.4-cm] thick, ring-shaped spacer plate located between the rotary table and the drive bushing. Pins on the torque meter fit into the rotary table, and holes in the torque meter accept the drive pins from the KB. Fig. 4 shows the prototype torque meter.

The body of the torque meter was machined from steel. Kelly drive pins were attached using the same pro-cedure used in the manufacture of drive bushings. Holes to accept Kelly drive pins were bored and fitted with wear bushings.

The torque path within the torque meter is from the four drive pins to the four wear bushings. Within the steel body, compressive and tensile forces are generated in front of and behind the drive pins, respectively. Strain in the steel resulting from these forces can be measured with strain gauges.

To increase strain to measurable levels, eight load-bearing webs were created within the solid steel struc-ture. These eight webs are oriented between drive pins and wear bushings. Two strain gauges are used on each web, top and bottom, and are connected in parallel. Each parallel pair is wired in series with the pair situated diametrically opposite to create one ann of the 350-ohm Wheatstone bridge. This strain-gauge bridge design is a conventional four-ann circuit with alternating tension and compression anns.

The net effect of this bridge arrangement is that web tension and compression are additive. When torque is applied, a signal is generated proportional to the torque. Because of the symmetrical arrangement of tension and compression gauges, the bridge negates side loads and reacts only to torque.

Telemetering the data is accomplished using an FM radio transmitter in conjunction with a custom-built radio frequency amplifier. Change in the strain signal is con-verted to a change in a subcarrier frequency. This infor-mation is transmitted through three radial antennas that are imbedded in fiberglass around the circumference of the torque meter. Transmission (carrier) frequency on the prototype torque meter is approximately 100 MHz [1 X 108 cycles/sec).

A dipole receiving antenna and an FM radio receiver receive and demodulate the signal. Output from the receiver is a direct current voltage that is proportional to torque. A strip-chart recorder provides a pennanent trace of the torque signal. The torque transducer is protected by a %-in. [1.9-cm] thick steel plate on top and a S-in. [0.9-cm] thick steel plate on bottom. Removable cover plates provide access to the battery power supply and to the transmitter package where the on/off switch is located. 990

Calibration of the instrument is accomplished using a special calibration frame capable of applying 50,000 ft-lbf [67 kN m] of known torque. Hydraulic cylinders are used with load cells to apply and measure the force at a known moment-ann length. This device allows easy recalibration to verify continued accuracy of torque readings. Field Use of Torque Meter. The torque meter is in-stalled between the table and drive bushing during a con-nection. The slips will fit through the center ofthe torque meter, and subsequent connections can be made with the torque meter in place. Drilling, working pipe, washing the floor, etc., can all be done virtually ignoring the presence of the torque meter.

Static and dynamic torque data are recorded on a strip-chart recorder with a pennanent tract for a given period of drilling activity. As expected, the typical torque trace is not constant during drilling but rather includes oscilla-tions at various frequencies. In this paper, these oscilla-tions are ignored; all torque readings are average values.

Torque readings are taken at a variety of drilling con-ditions with various rotary speeds and WOB's. Changes in rotary speed have only a minor effect on mean torque values. WOB, particularly in deeper, deviated wells, also tends to have a small effect on torque levels. This may result from the counteracting effects of increased bit torque and decreased string weight (and thus decreased friction) when WOB is increased. Friction Coefficients From Field Data Three examples are given that show the calculated fric-tion coefficients from accurate surface torque and drag data. Table 1 shows tabulated infonnation about each well, including details of the drill string and the direc-tional profile, as well as measured loads and calculated friction coefficients. Example 1. Well No.1 was drilling at 9,790 ft [2984 m] when torque and drag readings were taken. The well configuration was a 32 0 [0.56-rad] average angle build-and-hold profile with the kickoff point at 1,000 ft [305 m). A seawater-base drilling fluid of 11.6 Ibm/gal [1389 kg/m3] was used. Seventy percent of the hole was cased.

Pickup drag was 49,000 lbf [218 kN] over the rotating string weight of 153,000 lbf [681 kN]. Slack-off drag was 31,000 lbf [138 kN] less than string weight. Using the computer program, these loads reduced to a friction coefficient of 0.28 for pickup and -0.27 for slack-off.

Torque readings both on and off bottom oscillated in-tennittently with a mean value of 15,900 ft-Ibf [21 KN . m]. The detennination of a friction coefficient from this torque is complicated by the presence of drillpipe rubbers in the cased section of the hole. The characteristic radius of the drill pipe was increased in consideration of these rubbers to a value slightly greater than that for 4 V2-in. [11.4-cm] drillpipe with 6S-in. [16.2-cm] tool joints. The resulting sliding friction coef-ficient was calculated to be 0.27. Example 2. Well No.2 was a deep, relatively low-angle well. When readings were taken, an 8V2-in. [21.6-cm] hole was being drilled at 15,573 ft [4746 m], below 12,900 ft [3932 m] of9Ys-in. [24.4-cm] casing. The hole was kicked off at 3,000 ft [914 m] to a build-and-hold well profile with 24 0 [0.42-rad] average angle. This par-ticular hole was relatively free of doglegs.

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TABLE 1-FRICTION COEFFICIENTS FROM FIELD DATA

Well No.1 Depth, ft 9,790 Percent of hole cased, % 70 Drillstring 124 ft of 73f4-in. DC

990 ft of 41J2-in. HW 8,676 ft of 41f2-in. DP

Well profile build and hold Kick-off paint, ft 1,000 Average angle, degrees 32 Maximum angle, degrees 37 Mud weight, Ibm/gal 11.6 Rotating string weight, Ibf 153,000 Pickup weight, Ibf 202,000 Slack-off weight, Ibf 122,000 Rotating torque, ft-Ibf 15,900

Pickup 0.28 Slack-off -0.27 Rotating 0.27

The pickup weight of 377,000 lbf [1676 kN] was reduced to a friction coefficient of 0.31 using the com-puter program. A slack-off string tension of 232,000 lbf [1031 kN] produced a coefficient of -0.3L

Torque readings, both on and off bottom, were ap-proximately 18,300 ft-Ibf [25 kN m]. Torque was fairly constant with only small oscillations synchronous with rotary speed. Drillpipe rubbers were used in the cased portion of the hole with greater frequency of use near surface. If the extra effective radius was considered, the torque reading produced a sliding friction coefficient of 0.29.

Example 3. Well No.3 was a case in which high torque and drag were experienced during and after drilling out a 9Ys-in. [24.4-cm] casing shoe at 12,100 ft [3688 m]. The

2000

4000

t; ~ 6000 UJ Cl Cl UJ a: ~ 8000 UJ :;:

10.000

1~IW ANGLE

I HEAVY -WEIGHT PIPE AND

\ DRILL COLLARS

PICK-UP

WELL No.3

14.0000'-------1-oo---~2DO----300----4DO-----.J500

TENSION IN DRILL STRING Ix 1000 LBS'

Fig. 5-Drillstring tension vs. depth from Well No.3.

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Well No.2 Well No.3 15,573 12,200

83 99 458 ft of 63i4-in. DC 372 ft of 61f2-in. DC 15,115 ft of 5-in. DP 840 ft of 5-in. HW

10,988 ft of 5-in. DP build and hold build and hold

3,000 2,400 24 44 27 49

12.5 9.8 290,000 218,000 377,000 376,000 232,000 141,000 18,300 24,500

0.31 0.40 -0.31 -0.40

0.29 0.39

build-and-hold well profile was kicked off at 2,400 ft [731.5 m] to an average angle of 44 [0.77 rad]. The well had several severe doglegs of 4 and 6 per 100 ft

[0~07 and 0.1 rad per 30.5 m] in the lower portion of the build zone.

Initially an attempt had been made to drill out the shoe while drillpipe rubbers were used to protect the casing and drillstring. However, the torque required to rotate was found to be more than 35,000 ft-Ibf [47 kNm]. This was beyond the capability of the rig rotary drive.

After the pipe was tripped to remove rubbers, the string could be rotated but only when surface tension was slacked off. Without WOB, rotation was impossible. With approximately 38,000 lbf [169 kN] on the bit, the string could be rotated with a mean rotating torque of 24,500 ft-Ibf [33 kN m]. With an estimated 2,000 ft-Ibf

0

2000

BUILD 4DOO ANGLE

t; ~6IJXl UJ Cl Cl UJ a:

~1IIlOO :;:

10.000

12.000 2000 FT -LBS ESTIMATED

BIT TORQUE

WELL No.3

14,0000'---------5000---10..-'..000---15,-00-0 --2-0.o-oo--2-5,00-0--30--',lIXl TORQUE IN DRILL STRING 1FT -LBI

Fig. 6-Drillstring torque vs. depth from Well No.3.

991

[2.7 kN m] bit torque, the remaining 22,500 ft-lbf [30 kN'm] resulting from friction was reduced to a sliding friction coefficient of 0.39.

Without drillpipe rubbers, the radius of the drillpipe for use in the program was determined to be two-thirds of the distance between pipe body radius and tool joint radius. This is a reasonable assumption when based on the hypothesis that two-thirds of the side load is sup-ported at the tool joints.

Like torque values, the pickup and slack-off drag values were very large. Pickup weight was 376,000 Ibf [1672 kN], which was 158,000 Ibf [702 kN] more than the calculated rotating string weight of 218,000 ft-lbf [295 kN m]. Rotating string weight was not recorded as it was impossible to rotate without WOB. The pickup weight value produced a friction coefficient of 0.40. Slack-off weight of 141,000 Ibf [620 kN] produced to a coefficient of -0.40.

Torque and Drag Profiles. Once a friction coefficient has been determined, it is interesting to use the computer model to calculate the load profiles along the length of the drillstring. Fig. 5 illustrates tension in the drill string as a function of depth for Well No.3. Three cases shown are pickup, rotating off bottom, and slack-off of the drillstring.

The tension profile while rotating off bottom (no axial movement) is a smooth curve. The slope of this curve at any point represents the product of the buoyed drill string weight per foot and the cosine of the hole inclination angle.

Axial movement of the pipe produces marked changes in drill string tension. The most notable changes occur in the build zone between 2,400 and 4,800 ft [731.5 and 1463 m] where noticeable doglegs are present. In par-ticular, the lower part of the build zone had extreme doglegs of up to 61100 ft [0.1 rad/30.5 m]. Rapid changes in tension occur in this area in both pickup and slack-off tension.

Because friction acts in an upward direction during slack-off, the slope of this curve illustrates the relative effects of friction and weight on the string tension. Be-tween 4,000 and 4,600 ft [1219 and 1403 m], because of the extreme doglegs, the upward friction force is greater than the increments of pipe weight, and the string tension actually decreases over this interval.

A torque profile during drilling is shown in Fig. 6 for the same well. Torque changes in the vertical section of the hole (0 to 2,400 ft [0 to 731.5 m]) are shown to be small because of small side forces. As with tension, torque changes are rapid in the angle build zone and more gradual in the hold-angle zone. The 2,000-ft-lbf [2.7 kN] bit torque shown is assumed.

Conclusions 1. Drillstring torque and drag are primarily caused by

simple sliding friction between the drill string and the wall of the hole.

2. The computer model presented in this paper is realistic.

3. Sliding friction coefficients in seawater-base mud typically lie between 0.25 and 0.40.

992

Acknowledgments

We thank Exxon Production Research Co. for permis-sion to publish this paper and Exxon Co. U.S.A. for their continued support and cooperation in collecting field data. Special thanks are extended to Lisa A. Beaudry, Hubert L. Morehead, and Paul H. La Marche for their contributions in developing this technique.

Both the torque meter and the hookload indicator were fabricated by Brewer Eng. Laboratories of Marion, MA; LaVerne F. Wallace and Roger W. Masson were the principal Brewer participants in this project and did most of the design work on both devices.

Reference

1. Dyer, N.D.: "Rotary Torque Indicator for Well Drilling Ap-paratus," U.S. Patent No. 3,664,184 (1972).

Nomenclature

Ff = sliding friction force acting on element, Ibf [N]

F n = net normal force acting on element, Ibf [N] Ft = axial tension acting at lower end of

element, Ibf [N] tJ.Ft = increase in tension over length of element,

Ibf [N] M = torsion at the lower end of element, ft-lbf

[Nm] tJ.M = increase in torsion over length of element,

ft-lbf [Nm] r = characteristic radius of drill string element, ft

[m] W = buoyed weight of drill string element, Ibf

[N] ex = azimuth angle at lower end of drill string

element, degrees [rad] tJ.ex = increase in azimuth angle over length of

element, degrees [rad] 8 = inclination angle at lower end of drill string

element, degrees [rad] tJ.8 = increase in inclination angle over length of

element, degrees [rad] if = average inclination angle of element,

degrees [rad] p, = sliding friction coefficient between

drill string and well bore

SI Metric Conversion Factors ft x 3.048*

Ibf x 4.448 222

"-Conversion factor is exact.

E-Ol E+OO

m N

JPT

Original manuscripl received in Society of Petroleum Engineers office Jan. 25, 1983. Paper accepted for publication July 2, 1983. Revised manuscript received Jan. 3, t 984. Paper (SPE 11380) first presented at the 1983 IADCISPE Drilling Conference held in New Orleans Feb. 20-23.

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